## Extended trees of graphs.(English)Zbl 0814.05027

The paper introduces the concept of an extended tree of a graph in the following way: Let $$G$$ be a finite connected graph. If $$G$$ is a tree, then the unique extended tree of $$G$$ is $$G$$ itself. If not, then $$G$$ contains a circuit and thus there exists a vertex $$v$$ on the circuit and a partition of the set of edges incident with $$v$$ such that the vertex splitting in $$v$$ according to the partition is not disconnecting. We perform the splitting according to one of the chosen two-element partitions. We repeat this procedure, until a tree is obtained. This tree is called an extended tree. The properties of these trees are studied.

### MSC:

 05C05 Trees

### Keywords:

extended tree; partition; vertex splitting
Full Text: